Ratio, proportion and rates of change worksheet — GCSE Higher

1.A metal has a density of 7.8 g/cm³. Work out the density of the metal in kg/m³.

2.A shop sells identical pens. The total cost, C pence, of n pens is given by C = 12n. Write the ratio n : C in its simplest form.

3.A cup of tea is cooling. Its temperature, in °C, is plotted against time, in minutes, since it was poured. At t = 4 minutes, the gradient of the tangent to the graph is −3.2. What does this tell you about the tea at t = 4 minutes?

4.A train journey takes 2 hours 15 minutes. A bus journey to the same place takes 3 hours 45 minutes. Write the time for the train journey as a fraction of the time for the bus journey, giving your answer in its simplest form.

5.An amount of money is shared in the ratio 1:2:3. The largest share is £90 more than the smallest share. Work out the total amount that was shared.

6.Two hikers' journeys are shown on separate distance-time graphs. Hiker A's graph has gradient 4.5 km/h. Hiker B's graph has gradient 3.2 km/h. Work out how much faster Hiker A walks than Hiker B, in km/h.

7.Two quantities, P and Q, are in inverse proportion. A graph is drawn with P on the vertical axis and Q on the horizontal axis. Write down which description fits the shape of this graph.

8.In a bag the ratio of red counters to blue counters is 7 : 4. Write the number of red counters as a fraction of the number of blue counters.

9.The volume of water in a paddling pool, in litres, is plotted against the time since the tap was turned on, in minutes. What are the units of the gradient of a tangent to this graph?

10.The amount of fuel left in a car's tank, F litres, is plotted against the distance travelled, d miles, and the points lie on a straight line. The line passes through (0, 45) and (150, 15). Work out the gradient of the line and say what it tells you.

11.A curve has equation y = x² + 2x. Work out the average rate of change of y with respect to x over the interval from x = 1 to x = 4.

12.A printer prints at a constant rate. The time taken to print a batch of forms is inversely proportional to the printer's speed, in pages per minute. Printing at 20 pages per minute takes 15 minutes. Work out how long the same batch takes to print at 25 pages per minute. Give your answer in minutes.

13.Tap A fills a swimming pool in 6 hours. Tap B pours water twice as fast as tap A. The time taken to fill the pool is inversely proportional to the rate of flow. Work out how long tap B takes to fill the pool.

14.A crate exerts a force of 84 N on the floor through a base with an area of 2.4 m². Work out the pressure on the floor, in N/m².

15.The density of a type of wood is 0.8 g/cm³. Work out the mass of a piece of this wood with a volume of 150 cm³.